Sharing my idea with a few writer friends, I got some comments and encouragement. Johne Cook posted this (and more) on his Facebook page:
So here's something cool and inexplicable: a friend you may know is doing a thing I can't exactly explain but which is seriously cool.
Now, the story (as it is) is done.
To experience this, you need to put on your literary forensics cap and start at the BOTTOM of the Twitter feed, with the OLDEST post first. Read from oldest to newest, keeping in mind that the Tweeter doesn't know he is in the middle of a story.
Here's the link:
Twitter changed how the page works, so if you see the character (MundaneOne) start a Tweet with @someone's name, that is a conversation, and you'll get more story if you open it up.
If anyone is interested, when I have more time, I'll post some comments here reflecting on the experience. Meanwhile, enjoy!